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What is Measurement? Strict definition: “any method by which a unique and reciprocal correspondence is established between all or some of the magnitudes of a kind and all or some of the numbers...” –Magnitude: a particular amount of an attribute –Attribute: a measurable property

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Loose Definition: “the assignment of numerals to objects or events according to rules” (presumably any rules). A numeral is any symbol other than a word.

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The Nominal Scale of Measurement The function of nominal scales is to classify - are arbitrarily assigned to name. Does not meet the criteria of the strict definition of measurement. Given two measurements, I can determine whether they are the same or not. Write you Banner ID on your paper money and put it in this bag.

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Ordinal Scale of Measurement the objects/events are arranged in serial order with respect to the property measured, that order is identical to the order of the measurements. Given ordinal data on two objects, we can state whether they have equal amounts of the attribute measured or, if not, which has the greater amount.

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The most common type of ordinal scale is that of rank order. I throw those bills out the window. My associate, outside, my associate, outside, ranks the students in order of how long it took them to retrieve their money, where rank 1 belongs to the student who most quickly retrieved her money.

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Ranks are Ordinal Data Minutes | 1 3 4 7 12 TIME |-Y---Y-Y-----Y---------Y-----> RANK | 1 2 3 4 5 For the ranks, we can say that 3 represents more time than 1, but we cannot honestly say that the difference between rank 3 and rank 1 (3 minutes) is the same as the difference between rank 5 and rank 3 (8 minutes).

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Interval Scale of Measurement The “Minutes” data on the previous slide. a change of 1 unit on the measurement scale corresponds to the same change in the measured attribute, no matter where on the measurement scale the change is. We can make statements about (a-b) versus (c-d).

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Ratio Scale of Measurement a true zero point – a score of 0 means that the object/event has absolutely none of measured attribute. With nonratio data we cannot make meaningful statements about the ratio of two measurements, but with ratio data we can.

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we cannot say that 20 degrees Celsius (interval scale) is twice as hot as 10 degrees Celsius we can say that 300 degrees Kelvin (ratio scale) is twice as hot as 150 degrees Kelvin

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Variables A variable is a quantity that can take on different values. A constant is a quantity that is always of the same value. Discrete variable - one for which there is a finite number of potential values which the variable can assume between any two points on the scale. Number of light bulbs in a warehouse; number of items correctly answered on a true-false quiz.

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Continuous Variable one which theoretically can assume an infinite number of values between any two points on the scale. Example: Weight of an object in pounds. Can you find any two weights between which there is no intermediate value possible?

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Categorical Variable similar to discrete variable, but usually there are only a relatively small number of possible values. Also called a grouping variable or classification variable. The categories may be nominal (female, male; red, green, blue, other) or they may be ordinal (final grade of A, B, C, D, or F).

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Nonexperimental Research Observational research “Correlational” is a confusing term best avoided. No variable is manipulated. Best not to use the terms “independent variable” and “dependent variable” Better to use “grouping variable” and “criterion variable.”

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Alcohol and Reaction Time Observation Participants = folks randomly sampled in downtown Greenville in evening. Grouping variable = have been drinking or not. Criterion variable = score on reaction time task. We cannot make a causal inference.

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Alcohol and Reaction Time Experiment Randomly assign participants to groups. One group drinks alcohol, the other not. IV = alcohol consumption DV = score on reaction time task We can make a causal inference.

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Causal Inference To infer that X is a cause of Y Show that X precedes Y. Show that X and Y and correlated. Rule out noncausal explanations. –establish prior equivalence of treatment groups –treat groups differently (manipulate IV) –demonstrate that groups differ on DV

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More Definitions Data - numbers or measurements collected as a result of observations. This word is plural. The single is “datum.” Population – in applied statistics, a population is a complete and well defined collection of measurements, aka scores. A population is often considered to be composed of an infinite number of cases.

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An example of a finite population is the amounts spent on lunch today by all students at ECU. Sample - a subset of population. For example, the amounts spent on lunch today by members of my classes is a sample from that the population defined above.

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Parameter - a characteristic of a population. These are typically symbolized with Greek symbols, such as  y for the population mean of variable Y. Statistic - A characteristic of a sample. These are typically symbolized with Roman letters. For example, the sample mean of variable Y can be symbolized as M Y or Roman letters

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Statistics are also called estimators, as these are typically used to estimate the value of population parameters. Descriptive Statistics - procedures for organizing, summarizing, and displaying data, such as finding the average weight of students in your statistics class or preparing a graph showing the weights.

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Inferential Statistics - methods by which inferences are made to a larger group (population) on the basis of observations made on a smaller group (sample). For example, estimating the average weight at ECU by finding the average weight of a randomly selected sample of ECU students.

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Rounding If the first (leftmost) digit to be dropped is less than 5, simply drop all unwanted digits. If the first digit to be dropped is greater than 5, increase the preceding digit by one.

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If the first digit to be dropped is 5 –and any non-zero digits appear anywhere to the right of the 5, increase the preceding digit by one. –and no non-zero digit appears anywhere to the right of the 5 if the preceding digit is even, simply drop all unwanted digits if the preceding digit is odd, increase it by one.